Coordinate descent beyond PR94: conditional κ = 5.279109590448e-5

[rohanarun]

A small coordinate refinement beyond #94 gives conditional κ = 329944349403/6250000000000000 = 5.279109590448×10⁻⁵, about 0.000299% above #94 and 0.000358% above #93. Exact bit saving: 52793882951577/10¹⁸. This is a small finite gain, not a breakthrough or practical speedup.

Starting with #93's complete physical words, reverse coordinates 0 through 3 at h23 and exchange 5/6 at h25. The h25 change independently matches Maxime Fleury's #94. The additional h23 reversal supplies this increment. Roles remain 26,387 / 34,772, physical width 130,417,912, total recursive rank 74,988,452,500. Every source/frame/output/scatter label is transported; all slot operations and paid copy, endpoint, cleanup and growth charges remain intact.

Full verification passed on ea640ec01daf16ebe9d3d0a6ca9e47bd7f8b7dd8: 92 isolated test modules, 20 historical patch checks, parent and own six-control suites, and fresh complete producer/profile regeneration. All 54 GitHub checks passed on that research commit. The run completed at 2026-10-08 23:11:14 UTC in 3,814.48 seconds, with no source drift. See research/aligned-coordinate-descent/validation.json for evidence hashes. Only the receipt and status documentation changed afterward. The focused gate passed independently in 155.18 seconds, including independent parent-chain regeneration, byte comparisons, ordinary and arbitrary-dirty replay in both orientations, complete fresh CRT profiles, six controls, two rational moment implementations, both next-grid exclusions, 47 strict constraints and seven margins. There are 2,752 source pins. The exact comparison rejects the complete paid lists of #93 and #94 at the new saving. Every #94 paid-profile field also agrees with our independently checked parent h23 and selected h25 profiles; no regeneration of #94's own producer is claimed.

The bounded Daytona search ran 32 workers, four move families with four seeds in each dimension and 16 proposals per worker. All workers passed. Floating-point scores guided selection; all 289 complete selected-axis combinations, including the parent, were compared with exact rational arithmetic. Finite search does not prove global optimality.

python3 research/aligned-coordinate-descent/verify.py --regenerate
python3 research/aligned-coordinate-descent/test_controls.py
make verify

The coordinate-transport argument and complete paid profile are in research/aligned-coordinate-descent/PROOF.md. All inherited analytic, ordered residual compiler, uniform all-size recursion, scalar overhead, routing, prime selection, exact recovery and fixed-tape hypotheses remain. The inherited Lean companion concerns #91's values, not this new exponent.

Credit Maxime Fleury with Codebuff assistance for #94's independent h25 refinement; Chafik Boukhalfa #91, Thomas DiFiore #74, Rohan Arun #78/#85/#93, eumemic, Rohan Garg, Avi Eisenberg, Dominik Scholz, Alejandro Zarzuelo Urdiales, and all inherited contributors and OpenAI. Original notices and licenses remain preserved. Prepared by Rohan Arun with OpenAI Codex assistance.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Further adjacent-flag selection and full composition.

Review and limits: Exact-head CI evidence; inherited analytic interfaces remain assumptions.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 641aae7baf14ae21b69145d54e8232bf20076fce. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.